Introduction - SAJMSsajms.iurc.edu.pk/issues/2017a/paper5.pdf · Lubna Maroof Attiya Yasmin Javid y Imtiaz Badshah z Abstract: This study investigates the performance persistence

Do Mutual Funds Remain Persistent? Evidence from Pakistan

Lubna Maroof ∗ Attiya Yasmin Javid † Imtiaz Badshah ‡

Abstract: This study investigates the performance persistence of 78 mutual funds of Pakistanfor the period 2009-2015. The sample period is divided into two sub-periods, based on movementof KSE 100 index closing value. A skilled manager is a manager who can outclass the market con-sistently during both sub-periods. This study first estimates outer performance, selectivity, markettiming and volatility timing skills using Capital Asset Pricing Model. The results show absence ofpersistence regarding Jensen alpha, selectivity and market timing skill. The study is making novelcontribution by investigating persistence in volatility timing skill. The result reveals week evidenceof persistence for volatility timing skill under four-index model.

Keywords: Persistence, contingency tables, market timing, volatility timing, Pakistan mutual funds.

Introduction

For the last two decades, an increasing trend of investing in emerging market has beennoticed among the investors. Mutual funds come up as a fast growing investment optionto expedite investor’s desire of making profits. A mutual fund is a collective venture inwhich small investors pool their money to buy securities. The fund is managed by afund manager, serving as an agent for the investors. The manager’s job is to analyse theeconomic, industry and government trends and then forecast the future earnings of thesefunds. These small investors, unaware of the technical complications of ‘market efficiency’,expect the fund managers to take care of their investments. If the fund managers areenriched with the superior information, it would be depicted in his forecasting skills.

Mutual funds offer the investors higher returns with minimal risks through portfoliodiversification. Investors are not interested in earning short term profits only, rather in longterm profits. So they are keen to know whether these profits are temporary or long term?Though the investors keep an eye on past performance of funds but they have great concernabout the future performance as well. In fact, the individual and institutional investors willopt the performance methods that can help them to select the funds providing higher futureresults. Therefore, it is important to investigate whether funds sustain their performanceor not? If performance of mutual funds in one period will be continued in the followingperiod, the phenomenon is termed as performance persistence (Muruganandan, 2013).

∗Corresponding Author: PhD Scholar, NBS, NUST, Pakistan. E-mail: [email protected]†Professor, PIDE, Islamabad.‡Assistant Professor, NBS, NUST, Islamabad.

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South Asian Journal of Management SciencesVol 11(1): 68-94, 2017DOI:10.21621/sajms.2017111.05

South Asian Journal of Management Sciences

The quest of persistence is of prime importance to investors. If there is an indicationof persistence in performance, the investors would incline towards funds with superiorpast performance and penalize poorly performers funds by taking out their investment. Ifinvestors find predictability in funds’ performance, may transfer their investments towardswinner funds to reap abnormal returns (Cuthbertson, Nitzsche, & OSullivan, 2008). Thereare numerous studies that examine persistence in performance of mutual funds (Brown,Goetzmann, Ibbotson, & Ross, 1992; Vicente & Ferruz, 2005; Babalos, Caporale, Kostakis,& Philippas, 2008; Mwamba, 2013; Goetzmann & Ibbotson, 1994), and come up withmixed results. Studies by Wermers (2003); Cremers and Petajisto (2009); Huij and Post(2011) find evidence of persistence. Others investigate the reasons behind the persistencephenomenon. Carhart (1997) finds relationship between persistence and momentum factorsand transaction costs. Gottesman and Morey (2007) find connection between persistenceand expense ratio. Hoberg, Kumar, and Prabhala (2016) find that persistence is moreprofound when mutual funds face less competition from its rivals.

Persistence is an important component of fund’s performance. As per efficient mar-ket hypothesis, no fund should outclass the market consistently on risk-adjusted basis.Emerging markets, like Pakistan are professed to be less efficient than developed marketsand so one might perceive that they provide more opportunities to fund managers to getabnormal returns as compared to developed markets. Mwamba (2013) argue that the mar-ket itself contains some irrational agents that lead to inefficiency of markets and investorshave heterogeneous expectations for risk and returns. This causes the fund managers toadjust their portfolios to opt for various investment strategies and trying to outclass themarket. On the other hand, investors are also keen to know whether funds with superiorperformance in the past will continue their behavior in the subsequent period.

It is important to consider that a fund manager can beat the market either by purechance or by skill. A chance-based performance will not continue while a skill-based per-formance will persist over episodes of time. So a purely chance based performance isthe probability that the manager will beat the market by luck only while skill-based per-formance is attributable to manager’s ability to beat the market through his selectivity,market and volatility timing skills (Arif & Jawaid, 2011).

Successful selectivity timing is defined as ability to select stocks that outperform othersecurities having similar level of non- diversifiable risk (Munoz, Vargas, & Marco, 2014).Market timing is defined as a strategy intended to improve performance by altering portfoliorisk over periods of time in response to expectations about future returns in particularmarkets (Heaney, Hallahan, Josev, & Mitchell, 2007). Busse (1999) defines volatility timingas ability of a manager to reduce market exposure in anticipation of increase in marketvolatility, keeping other factors being constant.

This study investigate the persistence using 78 Pakistan mutual funds, as the industryhas shown marvelous growth in number of funds and assets under management in recentlast past years. In Pakistan, the first Mutual fund was introduced in 1962. By November2015, the total number of funds operating in Pakistan has increased to 181 and net assetsgrown to Rs.291 billion (www.mufap.com.pk). Investigating persistence in a small anddeveloping market is a challenging chore as there are data limitations issues. Klapper andLove (2004) argues that mutual fund industry require market integrity and market liquidity

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for its growth. Market integrity refers to the phenomenon where there is no informationasymmetry and no one can take advantage of information they possess. Market liquidityrefers to the situation with low transaction cost and investors do not have to undergoany loss caused by large price movements. Emerging markets lack these phenomenon’sso the models applicable to developed countries have some limitations when applied tothe emerging countries. Therefore, this study would help the researchers to develop newunderstanding about the models applied to the emerging markets.

The Literature suggests several performance measures. Cortez, Paxson, and Armada(1999) argue that approaches like rank portfolio or regression (past performance on futureperformance) are not appropriate for small markets due to limitation of data availability.So we follow the contingency table. To cater various risk factors, mutual funds are cate-gorized into Winners or Losers using Jensen-alpha, Fama and French (1993) and Carhart(1997). Very few studies have been done to investigate the persistence phenomenon forfund manager of emerging markets and for Pakistani market, we found only one. Hameedand Wazir (2015) analyses the Pakistan mutual fund industry from 1995-2010 and do notfind persistence in performance and skills. Our study is different from previous study asthe data is extended to 2015 and also investigating the persistence of volatility timing skillfor the first time.

This study makes novel contribution by investigating persistence in volatility skill ofmutual funds using Pakistani market. To our knowledge, literature does not show any studyinvestigating persistence of volatility timing skill among mutual funds. Our results confirmthat week evidence for persistence phenomenon is present for volatility timing skills onlywhereas all funds remain inconclusive for performance, selectivity skill and market timingskills.

The rest of the paper is structured as follow. First, the relevant literature is reviewedin section two, which is followed by data used in the empirical analysis. The methodol-ogy that is employed for analysis is discussed in section three and empirical results andinterpretation are presented in section four. The last section concludes the study and givespolicy implications

Literature Review

The most relevant studies on persistence in performance are reviewed in this section.Grinblatt and Titman (1992) are among the pioneer studies evaluating the persistencephenomenon. They use monthly returns of 279 funds from 1974-1984. Dividing sampleperiod into two subsets comprising of 5 years, they find significant persistence in fundperformance both for best-performing and worst-performing funds.

Hendricks, Patel, and Zeckhauser (1993) analysed quarterly returns data of funds from1974-88. They define funds having consistent short-term abnormal performance as “Hothands”. However, they find little support for consistent funds having consistent superiorperformance and contrasting results for consistent under performers. They further showthat survivorship bias does not affect the persistence of mutual funds.

One of the major contributions is made by Carhart (1997). He finds that funds which

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have outperformed in the past year continue to outperform in the following year. How-ever, this performance advantage largely fades away over longer episodes of time. Carhartendorses this advantage to momentum factor, arguing that recent outer performers tendto hold stocks with strong momentum (winning record) on average, though they don’tessentially use a momentum strategy. The differences in expense ratios and transactioncosts also attributed to this short-term performance persistence phenomenon.

Another contribution is made by Wermers (2003) covering the US industry for theperiod 1975-1994. They find short-term persistence among the mutual funds. They alsohighlight the reasons contributing to this short term phenomenon. They held responsibleboth the fund managers and investors. They find that investors chase last-year out per-formers and managers also invest the cash inflows in winners funds so that they can keepon performing well. Similarly, losing managers are reluctant to sell low-return stocks sothese funds also continue to be losers.

Ferruz, Sarto, and Vargas (2004) find evidence of performance persistence while using207 Spanish mutual over period of 1994 to 2002. They use parametric and non-parametrictechniques to examine the possible presence of persistence. They also conclude that takinglonger historical data does not increase the level of persistence.

Babalos et al. (2008) conducts study on Greek mutual funds for the sample period1998 to 2004. They employ several regressions to measure the performance. They suggestthat intercept of Carhart measure proves to be the most appropriate performance measureas it caters impact of most of the strategies mentioned in the literature. They find thatperformance persistence weakens when more risk factors are taken into account. They fur-ther conclude that no persistence is found after 2001. The increase in foreign institutionalinvestors, “dilution effect” (funds flows towards past winners), improvement in regulatoryenvironment and more competitive fund industry are the possible reasons.

Abdel-Kader and Qing (2007) find evidence of performance persistence for winnersand losers over shorter period of time. They find similar results when uses the Jensen’salpha and Treynor ratio and concludes that it is indifferent to the choice of measure.Huij and Post (2011) use the rank portfolio approach to investigate persistence amongemerging market funds for the period 1993 to 2006. Their results reveal strong persistencein performance of funds, concluding that these markets are less efficient as compared todeveloped markets so active managers can reap more benefits out of it. They furtherconclude that winner funds contribute more towards the return spread so investors cantake advantage of “hot hands” effect by financing in more in recent winner funds. Therank-portfolio approach is not suitable for small sample size.

Su, Zhao, Yi, and Dutta (2012) fail to find any evidence of long term persistence for42 Chinese mutual funds for the time period 2002 to 2009. They investigate performancepersistence by calculating whether a fund outperform the market benchmark or not. Theydefine winner if a fund beats the market benchmark. They conclude that winners repeattheir performance during periods of negative market returns while losers maintain theirperformance during good market returns.

Mwamba (2013) examine the persistence of hedge fund managers’ skills for boom andrecession periods. They use 6500 hedge Fund managers across the world. The sampleperiod extends from January 1995 to June 2010. For analysis, they divide the sample

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period into four sub-sample periods to cater different economic cycles. They describe askilled manager as a manager who can outclass the market for two consecutive sub-sampleperiods. They use contingency table, chi-square test and cross-sectional auto-regressiontechnique to investigate persistence. They conclude that funds are able to outperform andthis is attributable more towards market timing skill during recovery phases.

Flam and Vestman (2014) analyse the persistence of performance and selectivity kill forSwedish mutual funds industry for the period ranges from 1993 to 2013. They argue thatpersistence may be outcome of skill, so they use bootstrap analysis to investigate. Theyfail to find persistence in performance and stock-picking skill. They argue that positive ornegative performance is attributable to good or bad luck only.

Basu and Huang-Jones (2015) analyse the performance and persistence by using dataof 498 mutual funds for the period 2000 to 2010 of emerging economies. They employrank portfolio approach, dividing funds into equally weighted deciles, placing winners intodecile 10 and losers to decile 1. A positive statistically significant difference between thetop and bottom decile alpha would confirm persistence. They conclude that persistenceexists mainly for poor performing funds. They also add that persistence weakens for longerholding period, suggesting that persistence is mainly observed over shorter periods. Therank portfolio approach of splitting funds into decile is suitable when large number of fundsare available.

Hameed and Wazir (2015) analyses Pakistani mutual funds from 1995-2010. They ex-amine the performance and manager skills for the sample period. They find that mutualfunds are not able to show any persistence regarding performance and skills of the man-agers. They argue that lack of persistence is a result of efficient mutual funds market andhence the prices adequately reveal all the available information. They split the sampleperiod into pre-financial and post financial crises era. However, we investigate persistenceusing median of market index as cut-point. So our sample period comprises of two sub-periods below the cut-point and after the cut-point.

Sun, Wang, and Zheng (2016) examine persistence hedge fund performance over theperiod 1994 to 2014. They conclude that funds with better downside returns outclass theirother rivals in the following periods. Whereas funds with high upside return under performtheir rivals in down markets and shows mixed results for future up markets. Their resultsconfirm persistence in fund markers in weak markets only.

Vidal and Vidal-Garcca (2016) conduct study on European countries for the year 1990-2015. The sample contains daily data for 2052 open-end mutual funds. They find signifi-cant short-term persistence for all the countries and both for top-decile and bottom-decilemutual funds. They argue that their results support both phenomenon “hot hands” (win-ners being followed by winners) and “Cold hands” (loosers being followed by loosers”).Matallın-Saez, Soler-Domınguez, and Tortosa-Ausina (2016) investigate performance per-sistence among US equity mutual funds for the period 1990 to 2015. They report persistencein mutual fund performance, more profound in best performing funds. They further findthat performance and persistence varies depending upon the sample period, as they donot find persistence for post financial crises, i.e. 2008 to 2015. They argue that persis-tence phenomenon is conditioned upon the sample period used, one possible reason for theinconclusive results previously reported in literature.

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Hoberg et al. (2016) investigate how competition among the funds affect the persistence?They use 3390 open-end US equity funds over the period 1980 to 2012. They develop a newmeasure of manager skill, “customized peer alpha”. They conclude that more competitionlimits the persistence phenomenon. They argue that intense competition will lead to fasttrading and exploits the alpha generating activities. These circumstances will make difficultfor the managers to beat other active managers.

Methodology

To explore performance persistence among the mutual funds, analysis begins with calculat-ing performance coefficients. First the simple CAPM model is used. It is further extendedto three-factor Fama & French model and four-factor Carhart model. Babalos et al. (2008)argue that Carhart intercept proves to be the most appropriate performance measure asit caters impact of most of the strategies mentioned in the literature. We provide resultsfor the single-index and four index model. Using the CAPM, the returns characteristics ofmutual funds can be calculated through the following equation:

Rpt −Rft = αp + β1(Rmt −Rft) + εit (1)

where Rpt represents the fund return at period t, Rft is the risk-free rate at period t,Rmt represents the market returns (benchmark) at period t. The coefficient β1 is system-atic risk, measures the relative risk of the portfolio to the benchmark, αp, Jensen’s alpha,measures the returns on a portfolio having zero covariance with the return on the bench-mark. We measure performance by Jensen alpha, regressing excess mutual fund returnsagainst the market returns.

Selectivity and Market Timing Skills

Following the Jensen alpha’s results, Treynor and Mazuy (1966) established the models toexamine the market timing skill. Using this skill, they argue that the managers can adjusttheir portfolios to predict the market. They can adjust their risky holdings to increase(decrease) the fund market beta in anticipation of an expected up (down) market. Asa result, the β fluctuates over time and is no longer stationary. Hence, the relationshipbetween mutual fund return and market return no longer remain linear. Treynor andMazuy (1966) extend the CAPM model by introducing the square return term into thebasic model. The model thus takes the following form

Rpt −Rft = αp + β1(Rmt −Rft) + ηi(Rmt −Rft)2 + εit (2)

Where αp represents the selectivity timing and η represents the market timing abilityand all other variables remain the same as in equation (1). The negative coefficient of thesquared term shows that mutual funds lack the ability to anticipate the market. Managerwith market timing skill will increase η during the up market and vice versa. Treynor andMazuy (1966) find that a positive η shows that the portfolio’s returns are more responsiveto large positive market returns. Here the intercept represents the selectivity skill. A fund

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manager lacking market timing skill, will only depend on selectivity skill to earn abnormalreturns.

Matallın-Saez et al. (2016) argues that results are sensitive to the model used or thebenchmark considered. We extend the model by incorporating Fama and French (1993)and then Carhart (1997) models due to their wide appreciation in Finance literature.Goetzmann, Massa, and Rouwenhorst (2000), In et al. (2014), who find that this multi-factor model improves market return timing coefficients by reducing measurement bias.

The model thus takes the following form:

Rpt −Rft = αp + β1(Rmt −Rft) + β2SMBt + β3HMBt + ηi(Rmt −Rft)2 + εit (3)

SMB 1 and HML 2 represent the size and book-to market portfolios respectively. Asignificant positive β2 portrays that size effect exists. While, a significant negative β2depicts that size effect does not exist. However, insignificant β2 mean that size factor failsto supplement any significant returns to the portfolio. A positive significant β3 depicts thatvalue effect exists. The presence of value effect shows that high book-to-market portfoliosare adding more portfolio returns than the low book- to-market portfolio. However, anegative significant β3 confirms that the growth effect exists, i.e. returns of the portfoliois attributable more by low book-to-market portfolio.

Carhart (1997) claims that one-year momentum in stock-returns has a significant impacton portfolio returns and thus modifies three-factor model by incorporating momentumfactor. Now the extended model takes the following form:

Rpt −Rft = αp + β1(Rmt −Rft) + β2SMBt + β3HMBt

+β4MOM − t+ ηi(Rmt −Rft)2 + εit

(4)

In above equation, MOM 3 captures the difference between past winners and losers. Apositive significant β4, is an expressions that momentum factor is adding more value tothe portfolio return. Whereas, a negative significant β4 shows that the past loser portfoliois adding more positive returns than the past winner portfolio (contrarian effect). So Se-lectivity timing and market timing will be calculated from equation 4.

Volatility Timing

Holmes and Faff (2004) develop a cubic model, based on the market timing model ofTreynor and Mazuy (1966) for exploring the volatility timing skill, using Australian mutualfund industry. They argue that volatility timing ability is reflected by a market exposurethat is impacted by market volatility. The easiest way is by estimating a time-varying betafor a specific fund, comprises of a mean beta and a component, depending on the squared

1 SMB = [1/3(Small Low+ Small Medium+ Small High)- 1/3 (Big Low+ Big Medium+ Big High)]2HML= [ 1/2( Small High+ Big High)-1/2(Small Low+ Big Low)]3MOM= [ 1

2 (Small Winner + Big Winner) - 12 (Small Looser + Big Looser)

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excess market returns. Therefore, by incorporating a time-varying beta component, theydevelop a cubic market model as per given in equation 5:

rit = αp + βirmt + γir2mt + δir

3mt + εit (5)

Where αp represents the fund’s security ability. βi represents sensitivity to the market,γi represents the fund’s market timing ability and a positive coefficient represents thesuperior market timing ability. δi is coefficient of volatility timing ability, a negativecoefficient is an indication of existence of volatility timing ability.

Following Fama and French (1993) and Carhart (1997), the above equation takes thefollowing form, by incorporating size, book-to-market and momentum factors:

rit = αi + βirmt + δir3mt + β2SMBt + β3HMBt + β4MOM − t+ εit (6)

Performance Persistence

In order to investigate the persistence in performance, we follow non-parametric measure i.econtingency tables. Contingency tables for the above mentioned performance measures areconstructed. Cortez et al. (1999) conclude that approaches like rank portfolio or regression(past performance on future performance) are not suitable for small markets due to limiteddata availability constraint.

For two-period persistence test, this study constructs contingency tables for winnersand losers (Mwamba, 2013). This test scrutinizes the frequency with which winners andloser funds remain in the same category in both time-periods. The median fund returns foreach investment category is calculated to categorize funds. To proceed, the mutual fundsare categorized as winners (W) or losers (L). A manager is defined as a winner (looser) ifthe performance measure (intercept term as result of his investment strategies) is higher(lower) than the median of all the performance measures in that category (Mwamba, 2013).

WW are defined as winners in two consecutive periods, LL are defined as losers in twoconsecutive periods. While winner in first period and loser in second period is denoted byWL, whereas, loser in first period and winner in second period is termed as LW. Perfor-mance persistence is evident if the statistical interference confirms that a greater numberof funds are categorized in the WW/LL groups compared to the other two. These tablesshow the probability of funds to be remained in the same category in the following period.Several statistical tests will be used to test whether performance persistence is strongenough. The null hypothesis states that performance in first period has no relation withperformance in subsequent period. Hence corresponding to an odds ratio of 1. The nullhypothesis of no persistence would be rejected if statistical results confirm that winners inone sub-period remain winner in second sub-period.

Three statistical methods are employed, testing a different facet of persistence. Thisstudy uses cross-product ratio (the Odds ratio) posited by Brown and Goetzmann (1995),Z-test posited by Malkiel (1995) and the chi-squared test by Kahn and Rudd (1995). First,

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the cross product ratio (CPR) is calculated using following formula:

CPR =(WW ∗ LL)

(WL ∗ LW )(7)

Equation (7) measures the ratio of the funds showing persistence in performance tothe ones lacking persistence. If significantly larger number of funds exists in the WW/LLcategories compared to the other two categories (WL or LW), it suggests that performancepersistence exists (Grinblatt & Titman, 1992). In other words, if the performance in thefirst period is unrelated to the performance in the subsequent period, it corresponds to aCPR of one. Therefore under hypothesis of no persistence, CPR would be equal to 1. Inorder to test the statistical significance, Z-test is conducted assuming sample is asymptoticnormally distributed. The standard error is calculated in the following manner.

σ =√

(1/WW ) + (1 +WW ) + (1 + LW ) + (1 + LL) (8)

Z-statistic is employed to confirm the significance of the CPR. It is calculated by di-viding the log Odd ratio by its standard error, shown by equation (8).

Z − Stats =Ln(CPR)

σ(LnCPR)(9)

The Z-values confirms the persistence for the specific time-period to be investigated.The value of Z-statistic greater than the critical value will lead to the rejection of the nullhypothesis, demonstrating that performance persistence exists.

The critical values of Z-stats for 1%, 5% and 10% are 2.575, 1.96 and 1.645 respectively.Carhart (1997) conclude that Chi-square statistics is more powerful and robust than

other estimation techniques, as it carefully tackle the survivorship bias. Hence we employchi-square test statistic to compare the observed frequencies for the four categories (WW,LL, WL, LW) with the tabulated frequencies. The test is given by Mwamba (2013):

Chi− square =(WW −D1)2

D1+

(WL−D2)2

D2+

(LW −D3)2

D3+

(LL−D4)2

D4(10)

where D1, D2, D3 and D4 can be calculated using following equations:

D1 =(WW +WL) ∗ (WW + LW )

N

D2 =(WW +WL) ∗ (WL+ LL)

N

D3 =(LW + LL) ∗ (WW + LW )

N

D4 =(LW + LL) ∗ (WL+ LL)

NThe Chi-square tabulated values for 1%, 5% and 10% significance level are 6.634897

3.841459 and 2.705543 respectively.

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Empirical Results and Discussion

This empirical study covers the period from December 2009 to May 2015. To assess theperformance persistence the entire sample period has been divided into two sub-periodsbased on the movement of KSE 100 index closing value, which is shown in Chart 1. Themedian of the KSE closing returns has been taken, dividing into sub-period 1 ranging fromDec 2009 to August 2012 and sub-period 2 from September 2012 to May 2015. So sub-period 1 and 2 contains 2.8 years. At the cut-point a remarkable difference can be observedin the market index behaviour. After the cut-point, a continuous increasing trend has beenobserved in the market index value.

Figure 1Movement of KSE 100 Index closing value for the period from December2009 to May 2015

Descriptive Statistics

This section presents the details of descriptive statistics of 78 Pakistan mutual fund excessreturns and market returns used in the study for the time period 2009-15. We haveconstructed equally weighted portfolio, Rp to make assessment of mutual funds at aggregatelevel.

Table 1 presents summary statistics for equally-weighted mutual fund excess returnsand market returns for the whole sample ranging from years 2009 to 2015. It has 66observations in total. The positive means return values of Rp indicates that mutual fundsis providing profits to its investors. On average, the mean returns of firms in the sample

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is 1.030 and ranges from -7.8754 to 14.1315. On average, the Rp, offering high standarddeviation seems to be more risky. The mutual funds industry offer larger excess kurtosisand more positive skewness as compared to the market returns. Panel A and B representssummary statistics for the sub-period 1 and 2 respectively. Sub-period 2 offers higherreturns both for the market and mutual funds. Sub-period 1 presents higher skewnessand larger excess kurtosis compared to sub-period 2. Table A1 in Appendix reports thenames and categories of mutual funds used in this analysis. Table A2, A3, A4 and A5 inAppendix.

Table 1Mutual Funds Returns for the period December 2009 to May 2015

Variables Definitions Obs Mean Maximum Minimum Std.Dev. Skewnes Kurtoss

Rp Return of Mutual funds 66 1.03 14.1315 -7.8754 4.2066 0.8321 4.6442Rm Return of Market 66 0.028 0.2011 -0.0994 0.0591 0.2811 3.8398

Panel A: Summary Statistics for the period December 2009 to August 2012

Variables Definitions Obs Mean Maximum Minimum Std.Dv Skewness Kurtosis


Panel B: Summary Statistics for the period September 2012 to May 2015

Variables Definitions Obs Mean Maximm Minimm Std.Dev Skewnes Kurtoss


reports the coefficients of Jensen alpha, selectivity, market and volatility timing respec-tively, obtained from equations (1), (4) and (6) using 78 mutual funds from Pakistan.

Then the winners/losers managers are recognized after comparing their coefficients withthe medians of the managers using same investment strategy. These are also reported intables 4, 5 and 6. Once the winners and losers are identified, it is easy to work out thepersistence in performance of mutual fund industry using two period performance per-sistence analysis. Three techniques are used to perform analysis: the contingence table,the chi-square statistics and the cross-sectional regression method. First, for the contin-gence table, we employ the cross product ratio and by comparing the Z-statistics value andcritical value will determine the persistence of fund managers.

Table 2 reports the CPR and Z-statistics for outer performance, the selectivity skill,the market timing and the volatility timing skills using single-index and four-index models.The row (1) reports the Z-stats of the contingency table of winners and losers portfoliosfor sub-period 1 and sub-period 2, based on Jensen alpha (outer performance) using single-index and four-index models. In case of no persistence, CPR value should be equal to 1and Z-stats value should be less than 1.96 at 5%. The CPR is 0.406 and Z-stats value is-1.940 for outer performance under single-index model. However under four-index model,the reported CPR and Z-stats is 1.056 and 0.120 respectively. The null hypothesis statesthere is no persistence in performance. Keeping this in view, the result indicates thatthe fund managers do not demonstrate persistence in outer performance in sub-period 1and sub-period 2 under single-index and four-index models. With 1% confidence level, weaccept the null hypothesis.

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Table 2CPR and Z-Statistics Value for Performance Persistence

Single-Index Four-Index

CPR value Z-Stats CPR value Z-Stats

Outperformance 0.406 -1.94 1.056 0.12

Selectivity 0.935 -0.149 0.762 -0.6

Market Timing 1.147 0.303 0.573 -1.223

Volatility Timing 1.407 0.754 2.362 1.859

This table reports the CPR and Z-statistics for outer performance, the selectivityskill, the market timing and the volatility timing skills using single-index, three-index and four-index models for 78 mutual funds of Pakistan. CPR denotes theCross Product Ratio and Z-stats represents the calculated Z-stats to makedecision about rejection of null hypothesis.

Row (2) exhibit the Z-stats of the contingency table of winners and losers for bothperiods, based on selectivity skill using single-index and four-index models. Under single-index model, the CPR is 0.935 and Z-stats is -0.149. The null hypothesis of no persistenceis accepted as the Z-stats score lies within the range of two tail Z-score. Hence these resultsdepict that fund manager lack persistence in selectivity skill. Same results are supportedwhen four-index model is used. Here, the reported CPR value is 0.762 and Z-stats is -0.600.These results also support that funds managers lack the persistence in selectivity abilityboth under single-index and four-factor models. We can say with 1% confidence level thatfund managers lack persistence in selectivity skill.

Row (3) illustrates the contingency table reporting the winners and losers for sub-period1 and sub-period 2, based on market timing skill when single-index and four-index modelsare used. The null hypothesis states that there is no persistence in market timing skillof fund managers. The CPR value is 1.147 and Z-stats value is 0.303, we cannot rejectthe null hypothesis as calculated Z-stats value is less than the critical value. Therefore,fund managers do not exhibit persistence in market timing skill. These results are furthersupported, when four-index model is used. Under four-index model, the reported CPR is0.573 and Z-stats is -1.223. These figures suggest that funds managers lack persistence inmarket timing skills.

Row (4) illustrates the contingency table reporting the winners and losers for sub-period 1 and sub-period 2, based on volatility timing skill. The null hypothesis states thatthere is no persistence in volatility timing skill of fund managers. Under the single indexmodel, the reported CPR is 1.407 and Z-stats value is 0.754, therefore cannot reject thenull hypothesis as calculated Z-stats value is less than the critical value. Therefore, a fundmanager fails to exhibit persistence in volatility timing skill. Under four index model, wefind little evidence of volatility timing at 10%. The CPR value and Z-stats under four-index model is 2.362 and 1.859 respectively. At 10% significance level, the value of Z-statsis higher than the critical value, so we find week evidence of persistence in volatility timing.

Table 3 computes the chi-square statistics for each manager’s skill for the sub- period1 and 2. These calculate chi-square values are then compared with tabulated chi-squarevalues for one degree of freedom.

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Row (1) illustrates the chi-square values for sub-period 1 and sub-period 2, based onJensen alpha (outer performance) under single-index and four-index models. The chi-square value for Jensen-alpha is 3.826 under single-index model. The null hypothesisstates there is no persistence in performance. The calculated value is greater than thetabulated value for 1%. Therefore, we can reject the null hypothesis. Keeping this in view,we can state with 99% confidence that the fund managers exhibit persistence in outerperformance for sub-period 1 and sub-period 2, under the single-index model. However,contrasting results are reported when four-index model is used. Under four-index model,the reported Chi-square value is 0.014. These figures suggest that funds managers lackpersistence in outer performance.

Table 3Chi-Square Statistics value

Single-Index Four-Index

Outperformance 3.826* 0.014

Selectivity 0.022 0.361

Market Timing 0.092 0.581

Volatility Timing 0.57 3.512*

This table reports the chi-square value for outer performance, the selectivity skill,,the market timing and the volatility timing skills using single-index, three-indexand four-index models for 78 mutual funds of Pakistan

Row (2) reveals the chi-square values for both periods, based on selectivity skill undersingle-index and four-index models. The null hypothesis of no persistence is accepted asthe calculated score is less than the associated values for all the significance levels. Bothindex-value models offer values less than the critical values. As a result, we can say with99% confidence level that the fund managers lack consistence in the stock-picking abilityand their outer performance is based on luck rather on skill.

Row (3) reports the chi-square value for sub-period 1 and sub-period 2, based on markettiming skill. Here the chi-square value is 0.092 and 0.581 under single-index and four-indexmodels respectively. As the calculated chi-square value is less than the critical values at 1%,5% and 10% significance level. These results suggest that we can reject the null hypothesiswith 99% significance level and confirm that fund manager’s lacks persistence in markettiming skills under all the estimation methods.

Row (4) reports the chi-square value for sub-period 1 and sub-period, based on volatilitytiming skill. The reported chi-square value is 0.570 as per the results of single-indexmodel. The calculated chi-square value is less than the critical values at 1%, 5% and 10%significance level. These results suggest that we cannot reject the null hypothesis with 99%significance level and confirm that fund managers do not possess persistence in volatilitytiming skills. Once again, the opposite behavior is noticed when Carhart four index modelis used. The calculated Chi-square value is 3.512, which is greater than the tabulatedvalue. Hence it can be concluded that the fund’s managers possess persistence in volatilitytiming at 10% confidence level.

80


In the nutshell, there is no evidence of persistence of mutual fund performance exceptlittle evidence for the volatility timing skill. The absence of performance and selectivitytiming is in line with Flam and Vestman (2014); Mwamba (2013). They report that positiveor negative performance is attributable to good or bad luck only. The lack of long-termpersistence is in consistent with literature (Carhart, 1997; Hameed & Wazir, 2015; Basu &Huang-Jones, 2015; Benos & Jochec, 2011) highlight various reasons for lack of long-termpersistence. The reasons can be an increase in management fee charged by good performingfunds or desire of successful managers to hunt for more lucrative opportunities.

Our results are also in line with Sun et al. (2016), who report consistency in fundsmarkets for weak markets only and not for strong markets. Our sub-period 2 is the boommarkets and so do not find evidence for persistence. Our results are also in agreement withMatallın-Saez et al. (2016) who report lack of persistence in post-financial era .i.e. 2008 to2015.

Conclusion

This study examines the persistence regarding the timing abilities of Pakistani mutualfunds. The monthly data of mutual funds is used for the period 2009 to 2015. As theindustry is still in its embryonic stage age, so this study is limited to a total of 78 openend funds. This study employs cross-product ratio (the Odds ratio), Z-test and the chi-squared test (1995). The results suggest that the industry lacks the persistence regardingperformance, selectivity skill and market timing skill. As far as volatility timing skills areconcerned, the study finds week evidence to support this skill under Carhart four indexmodel.

These results are consistent to the previous literature suggesting that persistence fadesaway with longer time horizons. The results are also in line with the view that emergingmarkets are less efficient than developed markets and they offer greater avenues for fundmanagers to get abnormal returns. Another possible explanation of no persistence canbe increased competition among the mutual funds managers. Persistence is not only tooutperform the benchmark but also the capability to generate and sustain the outer perfor-mance over the time horizon. Pakistan mutual fund is a small market in terms of numberof investors and there are less avenues for fund managers to exploit excess returns. Hoberget al. (2016) argue that outer performance over competitors is a signal of skill. Increasedcompetition makes it difficult for fund managers to outclass other active managers. Hence,this increased competition among the funds can reduce persistence. No doubt, competitionwithin the industry are important but when there are zero entry and exit costs.

The implications of this study are that it helps the managers to decide whether tocontinue their existing management style or switch to some new style. Another implicationis that investors can reap maximum from “hot-hands effect” by investing in recent winnersand making intelligent investment decisions. It is the need of an hour that the governmentshould intervene to help the mutual fund market. Steps should be taken to increase theinvestors’ base and provide healthy competition among the managers.

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https://doi.org/10.2139%2Fssrn.2737272

https://doi.org/10.2139%2Fssrn.2737272


Appendix

A1: Funds names and their categories

Code Funds name Category

R1 ABL Income Fund Income

R2 AKD Aggressive Income Fund Aggressive Fixed Income

R3 AKD Opportunity Fund Equity

R4 Al Ameen Islamic Aggressive Income Fund Shariah Compliant Aggressive Fixed Income

R5 Al Ameen Shariah Stock Fund Shariah Compliant Equity

R6 Al Meezan Mutual Fund Shariah Compliant Equity

R7 Alfalah GHP Alpha Fund Equity

R8 Alfalah GHP Income Fund Income

R9 Alfalah GHP Income Multiplier Fund Aggressive Fixed Income

R10 Alfalah GHP Islamic Income Fund Shariah Compliant Income

R11 Alfalah GHP Islamic Stock Fund Shariah Compliant Equity

R12 Alfalah GHP Stock Fund Equity

R13 Alfalah GHP Value Fund Asset Allocation

R14 Askari Asset Allocation Fund Asset Allocation

R15 Askari High Yield Scheme Aggressive Fixed Income

R16 Askari Islamic Asset Allocation Fund Shariah Compliant Asset Allocation

R17 Askari Islamic Income Fund Shariah Compliant Income

R18 Askari Sovereign Cash Fund Money Market

R19 Atlas Income Fund Income

R20 Atlas Islamic Income Fund Shariah Compliant Income

R21 Atlas Islamic Stock Fund Shariah Compliant Equity

R22 Atlas Money Market Fund Money Market

R23 Atlas Stock Market Fund Equity

R24 BMA Chundrigar Road Savings Fund Aggressive Fixed Income

R25 BMA Empress Cash Fund Money Market

R27 Faysal Asset Allocation Fund Asset Allocation

R28 Faysal Balanced Growth Fund Balanced

R29 Faysal Income & Growth Fund Aggressive Fixed Income

R30 Faysal Savings Growth Fund Income

R31 First Capital Mutual Fund Equity

R32 First Habib Income Fund Income

R33 First Habib Stock Fund Equity

R34 HBL Income Fund Income

R35 HBL Multi Asset Fund Balanced

R36 HBL Stock Fund Equity

R37 JS Fund of Funds Fund of Funds

R38 JS Growth Fund Equity

R39 JS Income Fund Income

R40 JS Islamic Fund Shariah Compliant Equity

85


A1: Funds names and their categories

Code Funds name Category

R41 JS Large Cap Fund Equity

R42 JS Value Fund Equity

R47 Lakson Equity Fund Equity

R48 Lakson Income Fund Income

R49 Lakson Money Market Fund Money Market

R50 MCB Cash Management Optimizer Money Market

R51 MCB DCF Income Fund Income

R52 MCB Pakistan Asset Allocation Fund Asset Allocation

R53 MCB Pakistan Islamic Stock Fund Shariah Compliant Equity

R54 MCB Pakistan Sovereign Fund Income

R55 MCB Pakistan Stock Market Fund Equity

R56 Meezan Cash Fund Shariah Compliant Money Market

R57 Meezan Islamic Fund Shariah Compliant Equity

R58 Meezan Islamic Income Fund Shariah Compliant Income

R59 Meezan Sovereign Fund Shariah Compliant Income

R60 NAFA Government Securities Liquid Fund Money Market

R61 NAFA Income Fund Income

R62 NAFA Income Opportunity Fund income

R63 NAFA Islamic Aggressive Income Fund Shariah Compliant Aggressive Fixed Income

R64 NAFA Islamic Asset Allocation Fund Shariah Compliant Asset Allocation

R65 NAFA Multi Asset Fund Balanced

R66 NAFA Savings Plus Fund income

R67 NAFA Stock Fund stock

R70 National Investment Unit Trust equity

R71 NIT ? Government Bond Fund Income

R72 NIT ? Income Fund Income

R73 Pak Oman Advantage Asset Allocation Fund Asset Allocation

R74 Pak Oman Advantage Islamic Income Fund Shariah Compliant Income

R75 Pak Oman Islamic Asset Allocation Fund Shariah Compliant Asset Allocation

R76 Pakistan Capital Market Fund Balanced

R77 Pakistan Cash Management Fund Money Market

R78 Pakistan Income Enhancement Fund Aggressive Fixed Income

R79 Pakistan Income Fund Income

R80 Pakistan Int’l Element Islamic Asset Allocation Fund Shariah Compliant Asset Allocation

R81 PICIC Energy Fund Equity

R82 UBL Liquidity Plus Fund Money Market

R83 Unit Trust of Pakistan Balanced

R84 United Growth & Income Fund Aggressive Fixed Income

R85 United Stock Advantage Fund Equity

86


A2: Jensen Alpha from Equation ( 1 )

Period 1 Period 2Median W/L Median W/L Winner/Loser

R2 -0.0031 W 0.00944 W WWR9 -0.00988 L 0.00894 W LWR15 -0.00911 W 0.0089 L WLR24 -0.00914 L 0.01195 W LWR29 -0.0053 W 0.00818 L WLR78 -0.00449 W 0.00849 L WLR84 -0.01458 -0.00911 L 0.00917 0.00894 W LWR13 -0.02564 L -0.01633 L LLR14 -0.0098 L -0.01243 W LWR27 -0.0135 L -0.01639 L LLR52 -0.01573 L 0.00252 W LWR73 -0.02052 -0.01573 L -0.00994 -0.01243 W LWR28 -0.02368 L -0.00847 L LLR35 -0.01373 W -0.01599 L WLR65 -0.01111 W -0.00607 W WWR76 -0.01489 L -0.00602 W LWR83 -0.01416 L -0.00853 L LLR86 -0.001 -0.01395 W 0.00568 -0.00727 W WWR3 0.00148 W -0.01957 W WWR7 -0.02069 L -0.02586 L LLR12 -0.02118 L -0.02665 L LLR23 -0.02211 L -0.01292 W LWR31 -0.01116 W -0.02579 L WLR33 -0.01846 W -0.02292 L WLR36 -0.01409 W -0.02501 L WLR38 -0.02128 L -0.02089 L LLR41 -0.0428 L -0.01534 W LWR42 -0.01609 W -0.00798 W WWR47 -0.01985 L -0.02075 L LLR55 -0.02465 L -0.01531 W LWR70 -0.0203 L -0.01062 W LWR81 -0.00831 W -0.01979 L WLR85 -0.01961 W -0.01774 W WWR67 -0.01477 -0.01973 W -0.01259 -0.01968 W WWR37 -0.0141 -0.0141 W -0.03034 -0.03034 W WWR1 -0.00622 L 0.00723 L LLR8 -0.00418 L 0.00599 L LLR19 -0.00798 L 0.00817 W LWR30 -0.00401 W 0.00818 W WWR32 -0.00319 W 0.00791 W WWR34 -0.0023 W 0.00753 W WWR39 -0.01394 L 0.00765 W LWR48 -0.00224 W 0.00819 W WWR51 -0.00352 W 0.00672 L WLR54 -0.00282 W 0.00701 L WLR61 -0.01105 L 0.00889 W LWR62 -0.00576 L 0.01067 W LWR66 -0.0041 L 0.00727 L LLR71 -0.0038 W 0.00735 L WLR72 -0.00379 W 0.00721 L WL

87


A2: Jensen Alpha from Equation ( 1 )

Period 1 Period 2

Median W/L Median W/L Winner/LoserR79 -0.00411 -0.00405 L 0.0073 0.007443 L LLR18 -0.0018 W 0.00703 L WLR22 -0.00466 L 0.0071 L LLR25 -0.0039 W 0.00757 W WWR49 -0.00325 W 0.00724 W WWR50 -0.00309 W 0.00676 L WLR60 -0.00507 L 0.00712 W LWR77 -0.00541 L 0.00711 L LLR82 -0.00488 -0.00428 L 0.00738 0.007117 W LWR4 -0.00847 L 0.00827 L LLR63 0.0068 -0.00083 W 0.00957 0.008918 W WWR16 -0.01185 W -0.01272 L WLR64 -0.00936 W -0.00407 W WWR75 -0.01309 L -0.00739 L LLR80 -0.02454 -0.01247 L -0.00394 -0.00573 W LWR5 -0.01415 W -0.01471 L WLR6 -0.01396 W -0.01188 W WWR11 -0.02351 L -0.01833 L LLR21 -0.01744 W -0.01151 W WWR40 -0.04814 L -0.01346 L LLR53 -0.0259 L -0.01197 W LWR57 -0.01668 -0.01744 W -0.01324 -0.01324 W WWR10 -0.00267 W 0.00543 L WLR17 -0.00338 W 0.00651 W WWR20 -0.00453 L 0.00708 W LWR58 -0.00381 L 0.00819 W LWR59 -0.00411 L 0.00588 L LLR74 -0.00367 -0.00374 W 0.00592 0.006212 L WLR56 -0.00353 -0.00353 W 0.00697 0.00697 W WW

88


A3: Selectivity skill from Equation ( 4 )

Period 1 Period 2 Winner/Loser

Median W/L Median W/LR2 -0.0099 W 0.00511 W WWR9 -0.0196 L 0.00427 L LLR15 -0.01441 L 0.00537 W LWR24 -0.01064 W 0.01261 W WWR29 -0.01086 W 0.00461 W WWR78 -0.00935 W 0.00363 L WLR84 -0.02293 -0.01086 L 0.00398 0.004609 L LL

R13 -0.02712 L -0.02087 L LLR14 -0.01517 W -0.01598 W WWR27 -0.01762 W -0.0207 L WLR52 -0.01833 W -0.00254 W WWR73 -0.02279 -0.01833 L -0.01701 -0.01701 W LW

R28 -0.02583 L -0.01185 L LLR35 -0.01809 W -0.01915 L WLR65 -0.01485 W -0.01009 L WLR76 -0.01866 L -0.00699 W LWR83 -0.01836 L -0.00989 W LWR86 -0.00313 -0.01822 W 0.00074 -0.00999 W WW

R3 -0.00245 W -0.02094 W WWR7 -0.02194 L -0.02923 L LLR12 -0.0228 L -0.03033 L LLR23 -0.02393 L -0.01815 W LWR31 -0.01389 W -0.02601 L WLR33 -0.01778 W -0.02637 L WLR36 -0.0158 W -0.02694 L WLR38 -0.0194 W -0.02191 L WLR41 -0.04555 L -0.01151 W LWR42 -0.01539 W -0.00177 W WWR47 -0.0206 L -0.02078 W LWR55 -0.02583 L -0.01659 W LWR70 -0.02012 L -0.00921 W LWR81 -0.0105 W -0.02442 L WLR85 -0.02406 L -0.02121 L LLR67 -0.01643 -0.01976 W -0.01575 -0.02107 W WW

R37 -0.01709 -0.01709 W -0.0453 -0.0453 W WW

89


A3: Selectivity skill from Equation ( 4 )

Period 1 Period 2 Winner/Loser

R1 -0.01224 L 0.00108 L LLR8 -0.01072 L -0.00019 L LLR19 -0.01288 L 0.00393 W LWR30 -0.0102 W 0.00416 W WWR32 -0.00996 W 0.00368 W WWR34 -0.0091 W 0.00356 W WWR39 -0.0191 L 0.00388 W LWR48 -0.00848 W 0.00335 W WWR51 -0.00991 W 0.00063 L WLR54 -0.01041 L 0.00017 L LLR61 -0.01887 L 0.00391 W LWR62 -0.01169 L 0.00649 W LWR66 -0.01013 W 0.00309 L WLR71 -0.01048 L 0.00174 L LLR72 -0.0103 W 0.00172 L WLR79 -0.01007 -0.01036 W 0.00165 0.003223 L WL

R18 -0.00813 W 0.00283 L WLR22 -0.0108 L 0.0029 W LWR25 -0.01041 W 0.00369 W WWR49 -0.00913 W 0.00281 L WLR50 -0.00994 W 0.00236 L WLR60 -0.01134 L 0.00296 W LWR77 -0.01074 L 0.00281 L LLR82 -0.01076 -0.01058 L 0.00363 0.002865 W LW

R4 -0.0152 L 0.00348 L LLR63 0.00134 -0.00693 W 0.00535 0.004416 W WW

R16 -0.01678 W -0.01869 L WLR64 -0.0141 W -0.00762 W WWR75 -0.01703 L -0.01323 L LLR80 -0.02687 -0.0169 L -0.00492 -0.01042 W LW

R5 -0.01872 W -0.01887 W WWR6 -0.01516 W -0.01892 L WLR11 -0.02619 L -0.02374 L LLR21 -0.02274 L -0.01792 W LWR40 -0.04926 L -0.00816 W LWR53 -0.02121 W -0.01614 W WWR57 -0.01959 -0.02121 W -0.02163 -0.01887 L WL

R10 -0.00889 W 7.34E-05 L WLR17 -0.00973 W 0.00254 W WWR20 -0.01139 L 0.00304 W LWR58 -0.0097 W 0.00222 L WLR59 -0.01015 L 0.00014 L LLR74 -0.0099 -0.00981 L 0.00232 0.002272 W LW

R56 -0.0097 -0.0097 W 0.00284 0.002841 W WW

90


A4: Marketing timing skill from Equation ( 4 )

Period 1 Period 2

Median W/L Median W/L Winner/LoserR2 2.03027 W 1.28723 W WWR9 2.90293 W 1.38838 W WWR15 1.58238 L 1.04929 L LLR24 0.44806 L -0.19544 L LLR29 1.66128 W 1.06028 L WLR78 1.4526 L 1.44547 W LWR84 2.49492 1.661283 W 1.53973 1.287228 W WWR13 0.44349 L 1.34677 W LWR14 1.60328 W 1.05311 L WLR27 1.23035 W 1.27966 L WLR52 0.77438 W 1.50309 W WWR73 0.68006 0.774382 L 2.09955 1.346765 W LWR28 0.64385 L 1.00222 W LWR35 1.30107 W 0.93936 L WLR65 1.117 L 1.19295 W LWR76 1.12516 W 0.28884 L WLR83 1.25518 W 0.40245 L WLR86 0.63471 1.12108 L 1.46793 0.97079 W LWR3 1.17233 W 0.40718 L WLR7 0.37366 L 0.99964 W LWR12 0.48423 L 1.09339 W LWR23 0.54436 W 1.55405 W WWR31 0.81608 W 0.0646 L WLR33 -0.20162 L 1.02363 W LWR36 0.50982 W 0.5718 W WWR38 -0.56082 L 0.30514 L LLR41 0.8211 W -1.13864 L WLR42 -0.20974 L -1.84446 L LLR47 0.22291 L 0.00835 L LLR55 0.35147 L 0.37969 L LLR70 -0.05218 L -0.41983 L LLR81 0.65234 W 1.37689 W WWR85 1.33102 W 1.03233 W WWR67 0.4935 0.488862 W 0.93786 0.489487 W WWR37 0.89413 0.894133 W 4.44491 4.444911 W WWR1 1.79935 L 1.82648 W LWR8 1.95428 W 1.83695 W WW

91


A4: Marketing timing skill from Equation ( 4 )

Period 1 Period 2

Median W/L Median W/L Winner/LoserR19 1.46394 L 1.26092 L LLR30 1.8485 L 1.19371 L LLR32 2.02229 W 1.25608 L WLR34 2.0321 W 1.17967 L WLR39 1.54146 L 1.11908 L LLR48 1.86617 L 1.435 L LLR51 1.90997 W 1.80874 W WWR54 2.26822 W 2.03178 W WWR61 2.33923 W 1.47902 W WWR62 1.77214 L 1.24164 L LLR66 1.80424 L 1.24087 L LLR71 1.99657 W 1.66923 W WWR72 1.94566 W 1.63114 W WWR79 1.78036 1.888069 L 1.67847 1.457009 W LWR18 1.88955 W 1.24863 W WWR22 1.83613 L 1.24741 L LLR25 1.94575 W 1.15127 L WLR49 1.75798 L 1.31687 W LWR50 2.04619 W 1.3056 W WWR60 1.8732 W 1.23757 L WLR77 1.59329 L 1.27739 W LWR82 1.75618 1.854661 L 1.11225 1.24802 L LLR4 2.01005 W 1.42289 W WWR63 1.63298 1.821513 L 1.25178 1.337333 L LLR16 1.4725 W 1.77534 W WWR64 1.41504 W 1.05375 L WLR75 1.17682 L 1.73572 W LWR80 0.6948 1.295933 L 0.29146 1.394734 L LLR5 1.36795 W 1.23653 L WLR6 0.35896 L 2.09114 W LWR11 0.79962 W 1.60762 W WWR21 1.58299 W 1.90465 W WWR40 0.33636 L -1.573 L LLR53 -1.40343 L 1.2408 L LLR57 0.86806 0.799619 W 2.49082 1.60762 W WWR10 1.86151 W 1.58999 W WWR17 1.89884 W 1.17915 L WLR20 2.04886 W 1.20002 L WLR58 1.75969 L 1.77332 W LWR59 1.80436 L 1.70403 W LWR74 1.85905 1.860276 L 1.06743 1.395002 L LLR56 1.84292 1.842924 L 1.22656 1.226555 L LL

92


A5: Volatility timing skill of Equation ( 6 )

Period 1 Period 2

Median W/L Median W/L Winner/LoserR2 11.6316 W 4.9018 W WWR9 16.1219 W 3.37917 W WWR15 7.02353 W 2.57427 W LLR24 7.86344 W -8.47963 L LLR29 9.3734 W 3.06634 W WLR78 7.85419 W 5.74008 W LWR84 13.8309 9.3734 W 7.32284 3.37917 W WWR13 1.66114 W 4.48093 W LLR14 11.1445 W 11.7635 W WWR27 9.25532 W 9.74017 W WWR52 6.34442 W 8.20235 W WLR73 2.54839 6.34442 W 15.5205 9.74017 W LWR28 1.38368 W 7.88296 W LWR35 9.09368 W 5.45267 W WLR65 5.1622 W 10.1519 W LWR76 7.10272 W 2.09135 W WLR83 8.00459 W 5.22339 W WLR86 5.96222 6.53247 W 6.17273 5.8127 W LWR3 10.1105 W 1.71937 W WLR7 2.22109 W 1.17539 W LLR12 5.48728 W 13.0821 W WWR23 5.75569 W 14.5879 W WWR31 6.67372 W 5.05747 W WWR33 0.57599 W 9.25141 W LWR36 5.46111 W 5.08689 W WWR38 0.2503 W 2.21697 W LLR41 -0.95297 L -4.54477 L LLR42 1.77549 W -12.2738 L LLR47 2.71476 W -0.76694 L LLR55 1.84558 W 4.65497 W LWR70 2.24603 W -3.07944 L LLR81 7.61814 W 3.53742 W WLR85 8.11969 W 11.3062 W WWR67 3.9131 3.31393 W 9.6035 4.0962 W WWR37 6.62687 6.62687 W 42.0909 42.0909 W WWR1 10.1717 W 6.24872 W LWR8 11.5377 W 7.16665 W WWR19 6.05761 W 3.68214 W LLR30 10.2019 W 3.88709 W LLR32 10.7532 W 4.38002 W WLR34 10.4384 W 3.9677 W WLR39 10.8581 W 4.07663 W WLR48 9.97883 W 5.17414 W LLR51 10.0049 W 7.24813 W LWR54 12.5381 W 8.65424 W WWR61 11.4223 W 6.77462 W WWR62 8.65818 W 5.57912 W LLR66 9.43437 W 4.09729 W LLR71 10.9247 W 7.45888 W WWR72 10.699 W 7.65932 W WWR79 9.54864 10.3201 W 6.72128 5.91392 W LWR18 10.0117 W 4.02845 W WLR22 9.42881 W 4.08263 W WWR25 9.8739 W 3.49041 W WLR49 9.19383 W 4.69055 W LW

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A5: Volatility timing skill of Equation ( 6 )

Period 1 Period 2

Median W/L Median W/L Winner/LoserR50 10.5922 W 4.79455 W WWR60 9.54183 W 4.05935 W WLR77 8.70999 W 4.59442 W LWR82 9.42517 9.48532 W 3.22164 4.07099 W LLR4 13.8284 W 6.05466 W WWR63 10.2069 12.0177 W 4.70795 5.38131 W LLR16 7.68724 W 16.67 W LWR64 8.12443 W 8.56017 W WLR75 8.41107 W 9.862 W WWR80 3.56253 7.90584 W -0.55805 9.21109 L LLR5 8.68968 W 11.9618 W WWR6 5.24371 W 17.9951 W WWR11 3.62807 W 5.11092 W LLR21 11.0777 W 18.171 W WWR40 -0.23046 L -6.66117 L LLR53 -3.42881 L 9.32582 W LLR57 6.76531 5.24371 W 21.8823 11.9618 W WWR10 10.9358 W 5.69432 W WWR17 10.1439 W 3.78954 W LLR20 10.8297 W 3.48628 W WLR58 9.18887 W 9.06014 W LWR59 9.81239 W 6.65236 W LWR74 11.6784 10.4868 W 2.94977 4.74193 W WLR56 10.8093 10.8093 W 4.01965 4.01965 W WW

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Documents

Introduction - SAJMSsajms.iurc.edu.pk/issues/2017a/paper5.pdf · Lubna Maroof Attiya Yasmin Javid y Imtiaz Badshah z Abstract: This study investigates the performance persistence